Nair–Tenenbaum bounds uniform with respect to the discriminant

By Kevin Henriot. Mathematical Proceedings of the Cambridge Philosophical Society, 2011

59 citations recorded by the source corpus.

Abstract For functions F satisfying a certain submultiplicativity condition and polynomials Q1, . . ., Qk in [X], Nair and Tenenbaum obtained an upper bound on the short sum $\sum_{x < n \leq x+y} F(|Q_{1}(n)|,\dotsc,|Q_{k}(n)|)$ with an implicit dependency on the discriminant of Q1 . . . Qk. We obtain a similar upper bound uniform in the discriminant.

Subfields: Algebra and Number Theory, Applied Mathematics, Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/220faecf11f0809aba47512f8e30ce5d368ffa54

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Citations in the corpus

Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method (2015, unknown): “Note that such a result could also be deduced from earlier work of Barban and Vekhov [2]; see also [34] for the most recent results on this topic.”
COUNTING THE NUMBER OF SOLUTIONS TO THE ERDŐS–STRAUS EQUATION ON UNIT FRACTIONS (2011, methodology): “One should in fact be able to establish a version of Theorem 7.1 in which the implied constant depends explicitly on the discriminant ∆(P) rather than on C by using the estimates of Henriot [28] (which build upon earlier work of Barban–Vehov [2], S. Daniel, ‘Uniform bounds for short sums of certain ”